Question

Identify the numeric order of these fractions and mixed numbers from smallest to largest: 4/6, 2 5/6, 2 1/2, 2 3/4
Responses

256
, 234
, 212
, 46
2 Start Fraction 5 over 6 End Fraction , 2 Start Fraction 3 over 4 End Fraction , 2 Start Fraction 1 over 2 End Fraction , Start Fraction 4 over 6 End Fraction

52
, 114
, 176
, 46
Start Fraction 5 over 2 End Fraction , Start Fraction 11 over 4 End Fraction , Start Fraction 17 over 6 End Fraction , Start Fraction 4 over 6 End Fraction

25
, 411
, 617
, 46
Start Fraction 2 over 5 End Fraction , Start Fraction 4 over 11 End Fraction , Start Fraction 6 over 17 End Fraction , Start Fraction 4 over 6 End Fraction

46
, 212
, 234
, 256

Answer 1

To compare the fractions and mixed numbers \( \frac{4}{6}, 2 \frac{5}{6}, 2 \frac{1}{2}, 2 \frac{3}{4} \), we first convert each mixed number to an improper fraction:

1. \( 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \)
2. \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)
3. \( 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \)
4. \( \frac{4}{6} = \frac{2}{3} \)

Now we need to convert all fractions to a common denominator or to decimal for easy comparison:

Let's convert them all to decimals:
- \( \frac{4}{6} = \frac{2}{3} \approx 0.6667 \)
- \( 2 \frac{5}{6} \approx 2.8333 \)
- \( 2 \frac{1}{2} = 2.5 \)
- \( 2 \frac{3}{4} = 2.75 \)

Now we can arrange them in ascending order:
1. \( \frac{4}{6} \approx 0.6667 \)
2. \( 2 \frac{1}{2} = 2.5 \)
3. \( 2 \frac{3}{4} = 2.75 \)
4. \( 2 \frac{5}{6} \approx 2.8333 \)

So, the order from smallest to largest is:
- \( \frac{4}{6}, 2 \frac{1}{2}, 2 \frac{3}{4}, 2 \frac{5}{6} \)

The corresponding response using your provided format is:
**46, 212, 234, 256**